Subcarrier intensity modulation (SIM) scheme is preferred due to efficient bandwidth usage superiority over other modulation techniques such as on-off keying (OOK), pulse position modulation (PPM). In this paper, we investigate the bit error rate (BER) performance of optical wireless communication (OWC) system using binary phase shift keying (BPSK) SIM in non-Kolmogorov turbulent atmosphere. We pay attention to the weak turbulence conditions by using Rytov approximation and considering that the receiver is a PIN photodetector. Propagating beam type is Gaussian. It is seen that BER performance of the BPSK SIM OWC is significantly affected from non-Kolmogorov power law exponent, load resistor, responsivity of the PIN photodetector, bandwidth, beam source size, turbulence strength and noise factor.